D_4型李代数的极大幂零子代数的自同构

Automorphisms of Maximal Nilpotent Subalgebra of Type D_4 Lie Algebra

假设R是特征非2的交换幺环,L是R环上的D4型典型李代数,N是李代数L的一个极大幂零子代数.如果是极大幂零子代数N的任意一个自同构,那么可以表示成=ωη hσvvgμf,其中ω,η h,σv,vg,μf分别是图自同构、对角自同构、内自同构、第二中心自同构、中心自同构.

Let R be a unital commutative ring of characteristic not 2, and L be a D4-type classical Lie algebra over R. Set N be a maximal nilpotent subalgebra of L. For any fixed φ∈ Aut （N）, it can be expressed as φ=ωηhσvvgμf, where ω, ηh ,σv, vg ,μf are graph, diagonal, inner, second central, central automorphisms respectively.